SOLUTION: please explain to me how you decide which sign (positive/negative)is assigned to each of the factored parts: Solve: 3x^2 = 2 - x. My text shows the factor as (3x-2) (x+1)= 0 I

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: please explain to me how you decide which sign (positive/negative)is assigned to each of the factored parts: Solve: 3x^2 = 2 - x. My text shows the factor as (3x-2) (x+1)= 0 I       Log On


   

Question 203897: please explain to me how you decide which sign (positive/negative)is assigned to each of the factored parts:
Solve: 3x^2 = 2 - x. My text shows the factor as (3x-2) (x+1)= 0 I thought that when the constant is negative (i.e. 3x^2 + x - 2 = 0), you need a positive & negative sign. You determine which by assigning the sign of the "b" constant to the larger absolute value.
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+=+2+-+x Start with the given equation


3x%5E2+%2Bx-2=0 Add "x" to both sides. Subtract 2 from both sides.


Now let's factor 3x%5E2%2Bx-2


Looking at the expression 3x%5E2%2Bx-2, we can see that the first coefficient is 3, the second coefficient is 1, and the last term is -2.


Now multiply the first coefficient 3 by the last term -2 to get %283%29%28-2%29=-6.


Now the question is: what two whole numbers multiply to -6 (the previous product) and add to the second coefficient 1?


To find these two numbers, we need to list all of the factors of -6 (the previous product).


Factors of -6:
1,2,3,6
-1,-2,-3,-6


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -6.
1*(-6)
2*(-3)
(-1)*(6)
(-2)*(3)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 1:


First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1



From the table, we can see that the two numbers -2 and 3 add to 1 (the middle coefficient).


So the two numbers -2 and 3 both multiply to -6 and add to 1


Now replace the middle term 1x with -2x%2B3x. Remember, -2 and 3 add to 1. So this shows us that -2x%2B3x=1x.


3x%5E2%2Bhighlight%28-2x%2B3x%29-2 Replace the second term 1x with -2x%2B3x.


%283x%5E2-2x%29%2B%283x-2%29 Group the terms into two pairs.


x%283x-2%29%2B%283x-2%29 Factor out the GCF x from the first group.


x%283x-2%29%2B1%283x-2%29 Factor out 1 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28x%2B1%29%283x-2%29 Combine like terms. Or factor out the common term 3x-2


So 3x%5E2%2Bx-2 factors to %28x%2B1%29%283x-2%29.


Note: the order of the factors does not matter.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you are correct

if you have correctly transcribed the information from the text, then there appears to be an error in the book